Note that for \(v_{\rm max}=\sqrt{2\Delta m/m_e}\gg v_0\)  (the most probable velocity), we get \(\int _{0}^{v_{\rm max}}f(v) dv\simeq 1\) . In practice, the electron recoil energy is not manifested as a Dirac delta function but rather smeared by the detector resolution. This can be modeled by [1]}
\(\sigma _r=a\sqrt{E_R}+b ~E_R,\) 
